Details

analyze514.0ms (12.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.1%	0.1%	7
35.9%	64%	0.1%	8
47.2%	52.7%	0.1%	9
52.1%	47.8%	0.1%	10
65.3%	34.5%	0.1%	11
71.4%	28.4%	0.1%	12
74.2%	25.6%	0.1%	13
81.7%	18.1%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (34.4%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify137.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

2495×	`fma-neg_binary64`
1241×	`fma-def_binary64`
1051×	`div-sub_binary64`
520×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	20	18
2	31	18
3	48	18
4	71	18
5	103	18
6	155	18
7	209	18
8	270	18
9	300	16
10	389	16
11	599	16
12	934	16
13	1583	16
14	1525	16
15	1839	16
16	1745	16
17	1773	16
18	1933	16
19	2758	16
20	3102	16
21	4012	16
22	4885	16
23	4851	16

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	0.0b	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
✓	0.1b	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
✓	0.3b	(/.f64 -5641895835477563/5000000000000000 y)

series137.0ms (3.4%)

Counts

4 → 108

Calls

4 calls:

83.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
40.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
12.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
2.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
3.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
2.0ms	(/.f64 -5641895835477563/5000000000000000 y)
0.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)

simplify103.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-/l*_binary64`
549×	`fma-def_binary64`
209×	`distribute-rgt-in_binary64`
152×	`associate-/l/_binary64`
149×	`distribute-lft-in_binary64`

Counts

193 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	4154
1	654	3971
2	1995	3895
3	5228	3895

prune130.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	159	4	163

Error

Counts

163 → 4

Alt Table

Status	Error	Program
	24.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	13.5b	(+.f64 x (cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3)))
▶	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 3805 to 2381 computations (37.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	0.6b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	7.8b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series78.0ms (1.9%)

Counts

4 → 112

Calls

4 calls:

33.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
33.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
8.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
3.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
5.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
4.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
3.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

simplify144.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
270×	`fma-neg_binary64`
253×	`associate-/r/_binary64`
229×	`cancel-sign-sub-inv_binary64`
155×	`associate-/l/_binary64`

Counts

196 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	4366
1	671	4279
2	2246	4156
3	4858	4146
4	4953	4146

prune161.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	208	4	212

Error

Counts

212 → 4

Alt Table

Status	Error	Program
	24.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	13.5b	(+.f64 x (cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3)))
✓	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 4833 to 2491 computations (48.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
✓	0.2b	(pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3)
	0.3b	(/.f64 -5641895835477563/5000000000000000 y)
✓	29.5b	(cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3))

series216.0ms (5.4%)

Counts

2 → 72

Calls

2 calls:

146.0ms	(cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3))
70.0ms	(pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3)

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
32×	`cbrt-prod_binary64`
32×	`add-cube-cbrt_binary64`

Counts

2 → 92

Calls

2 calls:

7.0ms	(pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3)
3.0ms	(cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3))

simplify136.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-def_binary64`
348×	`unswap-sqr_binary64`
263×	`times-frac_binary64`
208×	`associate-/r*_binary64`
195×	`associate-/l*_binary64`

Counts

164 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	5464
1	900	4988
2	3544	4821
3	5098	4821

prune228.0ms (5.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	229	4	233

Error

Counts

233 → 4

Alt Table

Status	Error	Program
▶	24.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	13.5b	(+.f64 x (cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3)))
✓	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 6452 to 4420 computations (31.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	0.0b	(/.f64 y (exp.f64 z))
✓	0.2b	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))

series47.0ms (1.2%)

Counts

3 → 44

Calls

3 calls:

19.0ms	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
15.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))
13.0ms	(/.f64 y (exp.f64 z))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
13×	`associate-r_binary64`

Counts

3 → 79

Calls

3 calls:

6.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))
3.0ms	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
3.0ms	(/.f64 y (exp.f64 z))

simplify93.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

571×	`times-frac_binary64`
484×	`fma-neg_binary64`
321×	`fma-def_binary64`
246×	`associate-l_binary64`
236×	`cancel-sign-sub-inv_binary64`

Counts

123 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1506
1	373	1439
2	1004	1426
3	2907	1409
4	4794	1409
5	4963	1409

prune70.0ms (1.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	122	4	126

Error

Counts

126 → 4

Alt Table

Status	Error	Program
✓	24.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	13.5b	(+.f64 x (cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)) 3)))
✓	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 1818 to 831 computations (54.3% saved)

regimes250.0ms (6.3%)

Accuracy

Total 0.0b remaining (90.8%)

Threshold costs 0.0b (90.8%)

Counts

42 → 1

Compiler

Compiled 3490 to 2559 computations (26.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	12	16
2	12	16

end66.0ms (1.6%)

Compiler: Compiled 85 to 61 computations (28.2% saved)

Details

analyze514.0ms (12.9%)

sample1.4s (34.4%)

simplify137.0ms (3.4%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series137.0ms (3.4%)

rewrite13.0ms (0.3%)

simplify103.0ms (2.6%)

prune130.0ms (3.2%)

localize8.0ms (0.2%)

series78.0ms (1.9%)

rewrite23.0ms (0.6%)

simplify144.0ms (3.6%)

prune161.0ms (4%)

localize10.0ms (0.2%)

series216.0ms (5.4%)

rewrite17.0ms (0.4%)

simplify136.0ms (3.4%)

prune228.0ms (5.7%)

localize6.0ms (0.2%)

series47.0ms (1.2%)

rewrite15.0ms (0.4%)

simplify93.0ms (2.3%)

prune70.0ms (1.8%)

regimes250.0ms (6.3%)

simplify2.0ms (0.1%)

end66.0ms (1.6%)

Profiling